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Statistics and Probability Concepts
Elementary School
The student produces evidence that demonstrates understanding of statistics and probability concepts in the following areas; that is, the student:
a Collects and organizes data to answer a question or test a hypothesis by comparing sets of data.
b Displays data in line plots, graphs, tables, and charts.
c Makes statements and draws simple conclusions based on data; that is:
reads data in line plots, graphs, tables, and charts;
compares data in order to make true statements, e.g., “seven plants grew at least 5 cm”;
identifies and uses the mode necessary for making true statements, e.g., “more people chose red”;
makes true statements based on a simple concept of average (median and mean), for a small sample size and where the situation is made evident with concrete materials or clear representations;
interprets data to determine the reasonableness of statements about the data, e.g., “twice as often,” “three times faster”;
uses data, including statements about the data, to make a simple concluding statement about a situation, e.g., “This kind of plant grows better near sunlight because the seven plants that were near the window grew at least 5 cm.”
d Gathers data about an entire group or by sampling group members to understand the concept of sample, i.e., that a large sample leads to more reliable information, e.g., when flipping coins.
e Predicts results, analyzes data, and finds out why some results are more likely, less likely, or equally likely.
e Finds all possible combinations and arrangements within certain constraints involving a limited number of variables.

 

Middle School
The student produces evidence that demonstrates understanding of statistics and probability concepts; that is, the student:
a Collects data, organizes data, and displays data with tables, charts, and graphs that are appropriate, i.e., consistent with the nature of the data.
b Analyzes data with respect to characteristics of frequency and distribution, including mode and range.
c Analyzes appropriately central tendencies of data by considering mean and median.
d Makes conclusions and recommendations based on data analysis.
e Critiques the conclusions and recommendations of others’ statistics.
f Considers the effects of missing or incorrect information.
g Formulates hypotheses to answer a question and uses data to test hypotheses.
h Represents and determines probability as a fraction of a set of equally likely outcomes; recognizes equally likely outcomes, and constructs sample spaces (including those described by numerical combinations and permutations).
i Makes predictions based on experimental or theoretical probabilities.
j Predicts the result of a series of trials once the probability for one trial is known.

 

High School
The student demonstrates understanding of statistics and probability concepts; that is, the student:
a Organizes, analyzes, and displays single-variable data, choosing appropriate frequency distributions, circle graphs, line plots, histograms, and summary statistics.
b Organizes, analyzes, and displays two-variable data using scatter plots, estimated regression lines, and computer generated regression lines and correlation coefficients.
c Uses sampling techniques to draw inferences about large populations.
d Understands that making an inference about a population from a sample always involves uncertainty and that the role of statistics is to estimate the size of that uncertainty.
e Formulates hypotheses to answer a question and uses data to test hypotheses.
f Interprets representations of data, compares distributions of data, and critiques conclusions and the use of statistics, both in school materials and in public documents.
g Explores questions of experimental design, use of control groups, and reliability.
h Creates and uses models of probabilistic situations and understands the role of assumptions in this process.
i Uses concepts such as equally likely, sample space, outcome, and event in analyzing situations involving chance.
j Constructs appropriate sample spaces, and applies the addition and multiplication principles for probabilities.
k Uses the concept of a probability distribution to discuss whether an event is rare or reasonably likely.
l Chooses an appropriate probability model and uses it to arrive at a theoretical probability for a chance event.
m Uses relative frequencies based on empirical data to arrive at an experimental probability for a chance event.
n Designs simulations including Monte Carlo simulations to estimate probabilities.
o Works with the normal distribution in some of its basic applications.